{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:53:37Z","timestamp":1760237617261,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,5,29]],"date-time":"2020-05-29T00:00:00Z","timestamp":1590710400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the joint Ph.D. program of &quot;double first-rate&quot; construction disciplines of CUMT","award":["There is no number of this grant"],"award-info":[{"award-number":["There is no number of this grant"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The high noise of pseudorange and the ambiguity of carrier phase observation restrain the GNSS (Global Navigation Satellite System) application in military, industrial, and agricultural, to name a few. Thus, it is crucial for GNSS technology to integrate the pseudorange and carrier phase observations. However, the traditional method proposed by Hatch has obtained only a low convergence speed and precision. For higher convergence speed and precision of the smoothed pseudorange, aiming to improve positioning accuracy and expand the application of GNSS, we introduced a new method named MELS (Multi-Epochs Least-Squares) that considered the cross-correlation of the estimating parameters inspired by DELS (Double-Epochs Least-Square). In this study, the ionospheric delay was compensated, and so its impact was limited to the performance of the filters, and then exploited the various filters to integrate carrier phase observation and pseudorange. We compared the various types of Hatch\u2019s filter and LS (Least-Square) methods using simulation datasets, which confirmed that the types of LS method provided a smaller residual error and a faster convergence speed than Hatch\u2019s method under various precisions of raw pseudorange. The experimental results from the measured GNSS data showed that LS methods provided better performance than Hatch\u2019s methods at E and U directions and a lower accuracy at N direction. Nevertheless, the types of LS method and Hatch\u2019s methods improved about 12% and 9\u201310% at the 3D direction, respectively, which illustrated the accumulating improvement at the enhanced directions was more than the decreased direction, proving that the types of LS method resulted to better performance than the Hatch\u2019s filters. Additionally, the curve of residual and precision based on various LS methods illustrated that the MELS only provided a millimeter accuracy difference compared with DELS, which was proved by the simulated and measured GNSS datasets.<\/jats:p>","DOI":"10.3390\/rs12111762","type":"journal-article","created":{"date-parts":[[2020,6,2]],"date-time":"2020-06-02T09:19:27Z","timestamp":1591089567000},"page":"1762","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A Novel Dynamical Filter Based on Multi-Epochs Least-Squares to Integrate the Carrier Phase and Pseudorange Observation for GNSS Measurement"],"prefix":"10.3390","volume":"12","author":[{"given":"Fangchao","family":"Li","sequence":"first","affiliation":[{"name":"MNR Key Laboratory of Land Environment and Disaster Monitoring, China University of Mining and Technology, Xuzhou 221116, China"},{"name":"School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China"},{"name":"Nottingham Geospatial Institute, The University of Nottingham, Nottingham NG7 2TU, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingxiang","family":"Gao","sequence":"additional","affiliation":[{"name":"MNR Key Laboratory of Land Environment and Disaster Monitoring, China University of Mining and Technology, Xuzhou 221116, China"},{"name":"School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9013-4317","authenticated-orcid":false,"given":"Panos","family":"Psimoulis","sequence":"additional","affiliation":[{"name":"Nottingham Geospatial Institute, The University of Nottingham, Nottingham NG7 2TU, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2440-8054","authenticated-orcid":false,"given":"Xiaolin","family":"Meng","sequence":"additional","affiliation":[{"name":"Nottingham Geospatial Institute, The University of Nottingham, Nottingham NG7 2TU, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fuyang","family":"Ke","sequence":"additional","affiliation":[{"name":"School of Remote Sensing and Geomatics Engineering, Nanjing University of Information Science &amp; Technology, Nanjing 210044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,5,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00190-019-01330-1","article-title":"Speeding up PPP ambiguity resolution using triple-frequency GPS\/BeiDou\/Galileo\/QZSS data","volume":"94","author":"Geng","year":"2020","journal-title":"J. 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(1946\u20131975)"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/12\/11\/1762\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:33:52Z","timestamp":1760175232000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/12\/11\/1762"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,29]]},"references-count":39,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2020,6]]}},"alternative-id":["rs12111762"],"URL":"https:\/\/doi.org\/10.3390\/rs12111762","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2020,5,29]]}}}